Data Processing

The availability of the instantaneous PSF will make it possible to treat the fringe or speckle data differently from the usual methods. It will be possible to form coherent sums of the (Fourier transformed and phase-compensated) fringes or speckles from the science detector, without using the higher correlations (power spectra and bispectra) which result in higher order dependence on the object visibilites and the attendant difficulties for well-resolved objects. In summing data over say 10,000 frames (each about 10 ms) to reveal usable signals, it is assumed that the wavefront sensor receives an adequate signal in each frame, but its broad band operation and limited number of pixels used to receive each spot give a suitably faint limiting magnitude.

The first stage of data processing is the formation of the PSF from each data frame of the wavefront sensor. Marais et al. (1992) discuss a Fourier method which takes into account the discrete sampling imposed by the wavefront sensor lenslet array. In the cases where the telescope's central obstruction causes a gap in the wavefront sensor data, iterative model-fitting can be used to make the necessary one-parameter interpolation of the phase across the gap, but only for objects with simple structure. Similar methods have been verified in the processing of data from the present MAPPIT instrument. For complex objects, continuous wavefront sensor coverage along the aperture slit will be needed.

The second stage is the coherent summation of all exposures at one position angle. Information from the PSF is used to phase shift the fringes (or Fourier components of speckles) from the science detector back to standard registrations, so that the exposures can then be summed without having to detect the fringes or speckles in individual exposures. This process has been described by Primot et al. (1990) and Gonglewski and Dayton (1992). Enhancements to be used in the MAPPIT 2 procedure will be described in a later publication.

The result will be a 1-dimensional data set representing the true object as convolved with a smooth beam of width appropriate to the spatial resolution, with both additive and multiplicative noise. The noise in the estimate of the PSF from the wavefront sensor has the undesirable property that it depends on the object structure, but in practice it is not expected to be the dominant noise contribution.

The final stage of the process is to combine the separate 1-dimensional observations into a single image, using a conventional Fourier transform, and CLEAN or MEM techniques to remove the artifacts due to limited position angle sampling. The methods are well known, having been developed for processing data from linear radio synthesis arrays. In NRM mode, the data from MAPPIT 2 will form discrete points in the (u,v) plane, analogous to the data from a phase stable radio array. They will be distributed along radial spokes, but can be treated as a whole when making the image because the phase of each complex visibility point has been referred to a fixed zero point.

For study of barely resolved objects, it will be possible to examine individual fringe visibilities as a function of baseline by simply using the coherent sums of 1-dimensional Fourier transformed data at each position angle.

Calibration

The calibration procedure for the system will be a two-stage process. Firstly, observations of an unresolved pinhole at the coudé focus, with illumination by a tungsten lamp, will give wavefront sensor spot positions marking the zero points from which spot deviations will be measured. Likewise the fringe phase on the science detector gives the zero point for each baseline on that detector. The pinhole position in the focal plane thus becomes the zero phase reference position. This calibration procedure will remove the effects of lenslet imperfections and static aberrations of the telescope and optical system. Secondly, observations of unresolved standard stars will be used to determine the effects of residual visibility loss due to the non-zero sampling time and the non-zero spacing of the wavefront sensor elements across the aperture.

© Copyright Astronomical Society of Australia 1997